A list of numeric vectors containing edge ids.
Each vector is a minimum \((s,t)\)-cut.
partition1s
A list of
numeric vectors containing vertex ids, they correspond to the edge cuts.
Each vertex set is a generator of the corresponding cut, i.e. in the graph
\(G=(V,E)\), the vertex set \(X\) and its complementer \(V-X\),
generates the cut that contains exactly the edges that go from \(X\) to
\(V-X\).
Arguments
graph
The input graph. It must be directed.
source
The id of the source vertex.
target
The id of the target vertex.
capacity
Numeric vector giving the edge capacities. If this is
NULL and the graph has a weight edge attribute, then this
attribute defines the edge capacities. For forcing unit edge capacities,
even for graphs that have a weight edge attribute, supply NA
here.
Given a \(G\) directed graph and two, different and non-ajacent vertices,
\(s\) and \(t\), an \((s,t)\)-cut is a set of edges, such that after
removing these edges from \(G\) there is no directed path from \(s\) to
\(t\).
The size of an \((s,t)\)-cut is defined as the sum of the capacities (or
weights) in the cut. For unweighted (=equally weighted) graphs, this is
simply the number of edges.
An \((s,t)\)-cut is minimum if it is of the smallest possible size.
References
JS Provan and DR Shier: A Paradigm for listing (s,t)-cuts in
graphs, Algorithmica 15, 351--372, 1996.
# A difficult graph, from the Provan-Shier paperg <- graph_from_literal(s --+ a:b, a:b --+ t,
a --+ 1:2:3:4:5, 1:2:3:4:5 --+ b)
st_min_cuts(g, source="s", target="t")